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Odd and long; Computers aid a `prime' obsession.


For centuries, mathematicians have been playing with prime numbers.

Primes - positive integers divisible only by themselves and the number 1 - are one of those deceptively simple concepts that excite the mathematical imagination. Our brains seek patterns and interrelationships, and so the endless series of primes (2, 3, 5, 7, 11, 13, 17, etc.) has been poked and prodded for whatever secrets they possess.

Recently, in Missouri, a computer came up with the largest known prime number.

It's enormous, with more than 17 million digits. It is the number 2 multiplied by itself 57,885,161 times, minus 1. That "minus 1" is important, as every prime number beyond 2 has to be odd.

There are larger prime numbers, to be sure. There is an infinite number of primes, just as there's an infinite number of natural numbers - because, well, how could there not be?

Curtis Cooper, a computer science professor at the University of Central Missouri, did not let the 1,000 computers involved in the search rest with the discovery. He's searching for the next prime, which he expects to take years.

Mr. Cooper's quest is worth pausing to ponder. Applications are thin, beyond what conducting the search teaches computer experts. But finding a record-breaking prime number stretches our minds. It's amazing that a number so incredibly large has no divisors other than 1 and itself. Then, that an unending number of larger numbers can make the same lonely claim stirs us, thrillingly, to the edge of disbelief.

The jumbo prime discovered in January is noteworthy for a second reason. It's a Mersenne prime, in which the exponent of 2 (57,885,161 in this case) is also a prime number. This is only the 48th Mersenne prime known. But don't leap to the conclusion there's an infinite number of them; that's not settled in mathematical circles yet, according to the Internet.

The search for ever longer prime numbers will continue, in Missouri and elsewhere. Meanwhile, we're still trying to get a grasp on the smaller ones; and we wonder whether nature knows prime numbers are special, or only people do. That's an open question best left to scientists, number theorists, and idle afternoons.
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Title Annotation:EDITORIAL
Publication:Telegram & Gazette (Worcester, MA)
Article Type:Editorial
Date:Feb 27, 2013
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